On Fixed Marginal Distributions and Psychometric Network Models

Abstract

This reply addresses the commentary by Epskamp et al. (in press) on our prior work, of using fixed marginals for sampling the data for testing hypothesis in psychometric network application. Mathematical results are presented for expected column (e.g., item prevalence) and row (e.g., subject severity) probabilities under three classical sampling schemes in categorical data analysis: (i) fixing the density, (ii) fixing either the row or column marginal, or (iii) fixing both the row and column marginal. It is argued that, while a unidimensional structure may not be the model we want, it is the structure we are confronted with given the binary nature of the data. Interpreting network models in the context of this artifactual structure is necessary, with preferred solutions to be expanding the item sets of disorders and moving away from the use of binary data and their associated constraints.

Keywords:

• Network analysis
• sampling

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by National Institute on Alcohol Abuse and Alcoholism.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design.

Acknowledgments: The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors' institutions or the National Institute on Alcohol Abuse and Alcoholism is not intended and should not be inferred.

Notes

1 We note that we are addressing Epskamp et al (in press) assertions in reverse order as we feel the second assertion is a smaller issue than the first.

2 Although redundant, we introduce s to maintain a mneumonic structure for our notation as we find it helpful when interpreting the formulas that follow in the remainder of the presentation.

3 Given the values in the data matrix are required to be integers – specifically zero or one – such a matrix can be viewed as a contingency table where the maximum value of any of the table cells is constrained to be no larger than one.

4 In contrast, there are situations, such as exams, where we may expect a set of items to be interchangeable in their likelihood to have a positive endorsement.